7 min read•january 8, 2023
Krish Gupta
Daniella Garcia-Loos
Krish Gupta
Daniella Garcia-Loos
Current Density is a third way of describing the current in terms of the electric field, E, and the material it is traveling through. In this case, we define current density as a vector, J->. We then relate the electric field to the current density through the equation below. (For a full derivation of this equation, check out this link)
ρ is the proportionality constant between E and J and is called the resistivity. Resistivity describes how much a given material restricts the current. Resistivity depends on temperature (higher temperatures result in a higher resistivity, but most tables give values for 20 C)
Current density is a measure of the electric current flowing through a given area, while resistivity is a measure of the resistance of a material to the flow of electric current.
Here are some key points about current density and resistivity:
While resistivity describes how much a material restricts the current, resistance (R) is much more useful for describing a circuit. It takes into account the length (L) and cross-sectional area (A) of the conductor as well.
Resistance is defined as the opposition to current and can be a very useful feature when trying to design a circuit. For example, if the current gets too high in a cell phone, the battery starts expanding and can catch fire or explode.
Resistance is the property of a material or device to oppose the flow of electric current. It is a measure of the difficulty that the material or device presents to the flow of electric charges.
Here are some key points about resistance:
Because of Kirchhoff's rules, we can derive handy rules for resistors in series (Rs) and parallel (Rp) circuits.
Looking at these two equations we see an interesting phenomenon. As we add more resistors in series, the total resistance increases. However, adding resistors in parallel reduces the total resistance. An analogy that helps visualize this is relating this to check-out lanes at a grocery store. Even with the world's slowest cashier, opening another lane gets people out quicker than leaving them in a single line.
The basic mathematical relationship between resistance and current is defined by Ohm's Law. Depending on your context, it's written one of 3 ways. It doesn't actually matter which one you're more familiar with since they're all the same equation.
This law relates our three main circuit quantities in a nice simple equation. You will often see this represented in graphical form and be asked to infer if the device is Ohmic or non-Ohmic. As you can see in the graph below, an Ohmic device has a constant linear slope, while a non-Ohmic device does not. Sometimes a device can have an Ohmic region, then become non-ohmic.
Ohm's law is a fundamental principle in physics that describes the relationship between electric current, voltage, and resistance in an electrical circuit. It states that the electric current flowing through a conductor is directly proportional to the voltage applied to it and inversely proportional to the resistance of the conductor.
Here are some key points about Ohm's law:
1.
Choice B is correct. Because the resistance of a wire depends on \frac{\rho L}{A}AρL, a longer length and smaller area will result in the greatest resistance
Electrical circuits are often used to convert electrical energy into other types of energy. Recall from your previous physics classes that P = work/time. Using this, we can derive an equation for power in electrical terms.
Because of Ohm's Law we can also write this several different ways by subbing in V=IR or I = V/R. Choose the one that best fits the information that's given in the problem.
1. A hair dryer is rated at 1200W when connected to 120V. What is the resistance of the dryer?
As often happens with Physics problems, we idealize the 'real-world' problems away when we're doing calculations ("No air resistance", "Frictionless surface", "Ideal gasses", etc). When dealing with circuits, we tend to do this in 2 areas: wires & batteries. With wires, we assume (often correctly) that the resistance of the wires is insignificant to the total resistance of the circuit. However, with batteries, the internal resistance they exhibit is often large enough that we need to take it into account when we apply KVL and other circuit equations.
This leads to us defining a new term: Electromotive Force (EMF) represented by ϵ. EMF is the total energy that can be given to a charge leaving the cell and is related to the terminal voltage by the equation ϵ = VT + Ir, where r is the internal resistance of the battery.
Electromotive force (EMF) is the energy per unit charge that is available to drive electric current through a conductor. It is a measure of the electrical potential difference between two points in an electrical circuit.
Here are some key points about electromotive force:
Current Density
: Current density refers to the amount of electric current flowing through a given area. It is calculated by dividing the magnitude of the current by the cross-sectional area it passes through.Electromotive Force (EMF)
: EMF is the potential difference or voltage produced by a source such as a battery or generator. It represents the energy per unit charge that is converted from other forms of energy into electrical energy.Internal Resistance
: Internal resistance refers to the inherent resistance within a power source, such as a battery or generator, that limits the flow of current in a circuit.Kirchhoff's Rules
: Kirchhoff's Rules, also known as Kirchhoff's laws or circuit laws, are a set of fundamental principles used to analyze electrical circuits. They provide a systematic approach for solving complex circuits by applying the conservation of charge and energy.Power in Circuits
: Power in circuits refers to the rate at which electrical energy is transferred or consumed within an electrical system. It is measured in watts (W) and can be calculated using formulas involving voltage and current.Resistance
: Resistance is a measure of how much an object or material opposes the flow of electric current. It determines how difficult it is for electrons to move through a circuit.7 min read•january 8, 2023
Krish Gupta
Daniella Garcia-Loos
Krish Gupta
Daniella Garcia-Loos
Current Density is a third way of describing the current in terms of the electric field, E, and the material it is traveling through. In this case, we define current density as a vector, J->. We then relate the electric field to the current density through the equation below. (For a full derivation of this equation, check out this link)
ρ is the proportionality constant between E and J and is called the resistivity. Resistivity describes how much a given material restricts the current. Resistivity depends on temperature (higher temperatures result in a higher resistivity, but most tables give values for 20 C)
Current density is a measure of the electric current flowing through a given area, while resistivity is a measure of the resistance of a material to the flow of electric current.
Here are some key points about current density and resistivity:
While resistivity describes how much a material restricts the current, resistance (R) is much more useful for describing a circuit. It takes into account the length (L) and cross-sectional area (A) of the conductor as well.
Resistance is defined as the opposition to current and can be a very useful feature when trying to design a circuit. For example, if the current gets too high in a cell phone, the battery starts expanding and can catch fire or explode.
Resistance is the property of a material or device to oppose the flow of electric current. It is a measure of the difficulty that the material or device presents to the flow of electric charges.
Here are some key points about resistance:
Because of Kirchhoff's rules, we can derive handy rules for resistors in series (Rs) and parallel (Rp) circuits.
Looking at these two equations we see an interesting phenomenon. As we add more resistors in series, the total resistance increases. However, adding resistors in parallel reduces the total resistance. An analogy that helps visualize this is relating this to check-out lanes at a grocery store. Even with the world's slowest cashier, opening another lane gets people out quicker than leaving them in a single line.
The basic mathematical relationship between resistance and current is defined by Ohm's Law. Depending on your context, it's written one of 3 ways. It doesn't actually matter which one you're more familiar with since they're all the same equation.
This law relates our three main circuit quantities in a nice simple equation. You will often see this represented in graphical form and be asked to infer if the device is Ohmic or non-Ohmic. As you can see in the graph below, an Ohmic device has a constant linear slope, while a non-Ohmic device does not. Sometimes a device can have an Ohmic region, then become non-ohmic.
Ohm's law is a fundamental principle in physics that describes the relationship between electric current, voltage, and resistance in an electrical circuit. It states that the electric current flowing through a conductor is directly proportional to the voltage applied to it and inversely proportional to the resistance of the conductor.
Here are some key points about Ohm's law:
1.
Choice B is correct. Because the resistance of a wire depends on \frac{\rho L}{A}AρL, a longer length and smaller area will result in the greatest resistance
Electrical circuits are often used to convert electrical energy into other types of energy. Recall from your previous physics classes that P = work/time. Using this, we can derive an equation for power in electrical terms.
Because of Ohm's Law we can also write this several different ways by subbing in V=IR or I = V/R. Choose the one that best fits the information that's given in the problem.
1. A hair dryer is rated at 1200W when connected to 120V. What is the resistance of the dryer?
As often happens with Physics problems, we idealize the 'real-world' problems away when we're doing calculations ("No air resistance", "Frictionless surface", "Ideal gasses", etc). When dealing with circuits, we tend to do this in 2 areas: wires & batteries. With wires, we assume (often correctly) that the resistance of the wires is insignificant to the total resistance of the circuit. However, with batteries, the internal resistance they exhibit is often large enough that we need to take it into account when we apply KVL and other circuit equations.
This leads to us defining a new term: Electromotive Force (EMF) represented by ϵ. EMF is the total energy that can be given to a charge leaving the cell and is related to the terminal voltage by the equation ϵ = VT + Ir, where r is the internal resistance of the battery.
Electromotive force (EMF) is the energy per unit charge that is available to drive electric current through a conductor. It is a measure of the electrical potential difference between two points in an electrical circuit.
Here are some key points about electromotive force:
Current Density
: Current density refers to the amount of electric current flowing through a given area. It is calculated by dividing the magnitude of the current by the cross-sectional area it passes through.Electromotive Force (EMF)
: EMF is the potential difference or voltage produced by a source such as a battery or generator. It represents the energy per unit charge that is converted from other forms of energy into electrical energy.Internal Resistance
: Internal resistance refers to the inherent resistance within a power source, such as a battery or generator, that limits the flow of current in a circuit.Kirchhoff's Rules
: Kirchhoff's Rules, also known as Kirchhoff's laws or circuit laws, are a set of fundamental principles used to analyze electrical circuits. They provide a systematic approach for solving complex circuits by applying the conservation of charge and energy.Power in Circuits
: Power in circuits refers to the rate at which electrical energy is transferred or consumed within an electrical system. It is measured in watts (W) and can be calculated using formulas involving voltage and current.Resistance
: Resistance is a measure of how much an object or material opposes the flow of electric current. It determines how difficult it is for electrons to move through a circuit.© 2024 Fiveable Inc. All rights reserved.
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